The present invention concerns improvements relating to electrical power measurement and more particularly, though not exclusively, to a method of measuring an electrical power parameter, such as Apparent Power or Power Factor, which is accurate for single and multiple phases under all conditions namely those of balanced and unbalanced loads, and distorted and non-distorted waveforms.
The quantities that have conventionally been used to measure the quality and quantity of electric power are generally considered to be true and accurate when power is supplied to the load in a sinusoidal waveform and the load bears equally on each phase of the supply. The parameters that are widely used in power measurement are Active Power (P), Apparent Power (S), Reactive Power (Q) and Power Factor (PF).
Active power, when integrated in time, is used for billing purposes and reflects the energy consumed. Power Factor in AC circuits is a convenient figure of merit representing the utilisation of the supplying system by consumers and is used to determine the quality of the load. Reactive Power contributes to transmission losses and is used to define the oscillation of energy caused by reactive elements in the load. It is an important quantity in defining the current carrying capacity of electrical transmission systems, in the design of consumer plants and equipment and is often used in the calculation of Power Factor. Apparent Power is used to measure the maximum demand for industrial loads and it reflects the capital investment in the supplying systems. Apparent Power is also used in power engineering to define the maximum ratings of electrical apparatus, and in revenue metering, it is used as a meaningful quantity in the general power theory of electrical networks.
Of the above-mentioned quantities only the first, Active Power, is widely accepted as holding for unbalanced or non-sinusoidal situations. Reactive Power, Apparent Power and Power Factor become less valid when the supply is distorted or the load is unbalanced.
Non-linear and unbalanced loads are widespread and have caused concerns to electricity suppliers, users and regulators for many years. Non-linear loads have detrimental effects on components of the power system, they give rise to harmonic power flows to other users of the supply, and they contribute to a deterioration of the supply quality. Also, load imbalance in polyphase systems reduces the performance of the distribution system, causes voltage asymmetries which may be harmful for customers"" loads, and also contributes to a deterioration of the supply quality. In the absence of a proper system for power measurement for non-linear loads, various approximations and work-arounds are made. These are unsatisfactory from many points of view: consumers are not charged accurately, and equipment designers have to cope with a margin of error when their prototypes are tested, for example.
The lack of a universally accepted definition of Apparent Power, for example, leads to inconsistencies and inaccuracies in VA demand meters used for billing purposes. Meters from different manufacturers (or even different models by the same manufacturer) use different definitions of Apparent Power. Different operating principles may also be used. Each meter type therefore responds differently to different types of load, and no conventional meter gives consistent results for all loads. Under distorted waveform conditions their readings can differ by several percent even for the same balanced but non-linear, load. In extreme circumstances, the differences may be as high as 30%. Standard engineering text books tend to skate over this problem, but International institutions such as the EEC, IEEE and IEE are well aware of it.
Due to uncertainties in defining Reactive Power in non-sinusoidal situations, the use of Apparent Power is preferred in some countries for determining Power Factor. However, using existing standard power theory in AC circuits, Apparent Power itself cannot be defined consistently in an unbalanced three-phase system.
There is a considerable body of literature which describes the shortcomings of the current approach to calculating Apparent Power, Reactive Power, and Power Factor. Examples notable for their clarity are:
(1) A. Emanuel, xe2x80x9cOn the Definition of Power Factor and Apparent Power in Unbalanced Polyphase Circuits with Sinusoidal Voltage and Currents,xe2x80x9d, IEEE Trans. On Power Delivery, Vol. 8, No. 3, pp. 841-852, July 1993;
(2) P. S. Filipski, Polyphase xe2x80x9cApparent Powerxe2x80x94the Misleading Quantity In Non-Sinusoidal Power Theory: Are all Non-Sinusoidal Power Theories Doomed to Fail?,xe2x80x9d ETEP, Vol.3, No.1, pp. 21-26, January/February 1993; and
(3) R. West, xe2x80x9cThe Measurement of Apparent and Reactive Power with Unbalanced Loads and Non-Sinusoidal Waveformsxe2x80x9d, Distribution 2000 Conference, Sydney, 1997.
These authors described three key aspects of the problem Firstly, that there appears to be a good working definition in single-phase systems, where convention gives rise to calculated quantities to which one can attribute a physical meaning. Secondly, that there is a problem in polyphase systems of attributing a real physical meaning to the calculated parameters in existing theories. Intuitive reasoning appears to fail here. Thirdly, that the analysis of polyphase systems gives rise to no less than five different definitions for Apparent Power in three-phase systems with or without distorted waveforms. These results are often different by quite significant margins; particularly in unbalanced systems with distortion.
A good review of previous works has been presented in the paper by West (1997). The problems have been reported in many technical papers in for example by West (1997), Filipski (1993), Emanuel (1993), and in IEEE Working Group Report, xe2x80x9cPractical Definitions for a Powers in Systems with Non-Sinusoidal Waveforms and Unbalanced Loads: A Discussionxe2x80x9d, IEEE PWRD, Vol. 11, pp. 79-101., but yet no acceptable solutions have been found. The emphasis for calculating Apparent Power is now on System (equivalent) Apparent Power, see the papers by West (1997), Emanuel (1993), and IEEE Working Group Report. Also, the quantity know as RMS Apparent Power has also been considered by some technical institutions.
One of the main disadvantages with all the proposed methods for calculating Apparent Power is the fact that their results all depend on the voltage of reference point at which measurement is made. In single-phase circuits, the RMS values of voltage across the load and current through the load are clearly defined. However, in three-phase systems the Apparent Power should not depend on the reference voltage see paper by L. S. Czarnecki, xe2x80x9cPower Related Phenomena in Three-Phase Unbalanced Systemsxe2x80x9d, IEEE PWRD, Vol. 10, pp. 1168-1176. This disadvantage of the conventional power measurement methods is readily apparent by the following example of a three-phase system.
Considering FIG. 1, in a balanced situation, points 0, N1 and N2 have zero voltage. The RMS values of the phase voltages measured with respect to three references are the same which in turn it implies that the Apparent Powers are equal. However, if the load is unbalanced then N1, N2 and 0 have different voltages. Only 0 retains zero voltage. Thus, Apparent Power calculated using the voltages measured with respect to 0, N1, and N2 will be different.
Now consider a three-phase load that is supplied by an ideal source (Zs=0). Assume that one of the lines, say xe2x80x9ccxe2x80x9d, is broken (Ic=0). The measured voltage for phase xe2x80x9ccxe2x80x9d would be different on the sides of the broken point. If the voltage transducer is on the source side then it is the source voltage and if the potential transformer is on the load side, the measured voltage is influenced by the current of other two lines and the load impedance. Thus, the system (equivalent) Apparent Power (see papers by West (1997) and IEEE Working Group Report) will be different for the load.
One of the reasons for calculating Apparent Power is to obtain Power Factor. Consider now a single-phase circuit consisting of source with impedance Zs and a pure resistive load. Conventionally, Power Factor for this load is calculated to be unity. Assume that the above single-phase load is connected to a three-phase system with the same source impedance/phase as the single-phase system. For simplification of the analysis assume a perfect earthing, hence zero neutral impedance. Depending on the definition used different results are obtained for Power Factor as the calculated Apparent Powers are different. Phasor and RMS Apparent Powers are both equal to unity. The System Apparent Power would be less than one. Surely, as the full system capacity is not utilised by the load and also due to extra losses in the form of negative and zero sequence powers in the source impedance, a unity Power Factor is technically unacceptable. In other words, a unity Power Factor does not reflect the quality of the load and utilisation of the system (see papers by L. S. Czarnecki and Emanuel). The System Apparent Power does reflect this effect of a single-phase load connected to a three-phase supply. However, since the load itself, and thus its quality, has not changed then one may argue that Power Factor must remain the same. It is clearly seen by the above that there is an inconsistency in the approach, observation and result using conventional power theory in AC circuits.
It is an object of the present invention to overcome the above problems.
The inventor has determined that the cause of the problems observed for polyphase circuits lies in the basic characterisation applied to single-phase circuits, which is flawed. Though the results given for single-phase systems are acceptable in practice, the extension to polyphase systems strains the analysed and produces the difficulties such as misleading and inconsistent results which have been observed.
The inventor has developed a novel power measurement method based on a new approach which advantageously removes the uncertainty and ambiguity from present methods of power measurement. The new approach applies consistently across-the-board to balanced and unbalanced loads, linear and non-linear loads, single-phase and polyphase supplies, to sinusoidal and non-sinusoidal supplies, and which is consistent for all system topologies and conditions, does not violate any principle of electrical engineering and can be readily implemented in practical equipment. The basis for the present invention is a complete and self-consistent mathematical approach covering all measurement scenarios.
According to one aspect of the present invention, there is provided a method of measuring the value of an electrical power parameter, such as Apparent Power or Power Factor, of an electrical power signal the method comprising: calculating a first instantaneous power component as the product of an instantaneous voltage signal of the electrical power signal and an instantaneous current signal of the electrical power signal; carrying out a relative phase shift between the instantaneous voltage signal and the instantaneous current signal; calculating a second instantaneous power component as the product of the relatively phase-shifted instantaneous voltage and instantaneous current signals; RMS averaging each of the first and second power components to determine their respective magnitudes; and using both of the calculated magnitudes to determine the value of the electrical power parameter.
One of the advantages of the present invention is that it enables consistent measurement such that loads can be properly characterised, so that efficient engineering action can be taken, or accurate pricing adjustments can be made.
A utility embodying the present invention can offer accurate metering of these awkward loads can offer keener prices to attract the business of those customers whose loads are over-estimated by existing meters. It has a proper basis on which to raise its prices to customers whose loads have been underestimated, to reflect the true economics of supplying them. There are many other commercial benefits.
The new approach described herein redefines the nature of Reactive Power. On that basis, a new definition for Apparent Power is provided which is consistent for all circuit situations and topologies. The new definitions satisfy the rules of electrical engineering both in time and frequency domain.
In an embodiment of the present invention, a voltage signal is phase shifted by xe2x88x9290 to produce a quadrature axis voltage signal. By multiplying the original and quadrature voltages by a current signal, two instantaneous power signals are obtained. The former is an instantaneous active power component signal pp (t) and the latter is an instantaneous quadrature (reactive) power component signal pq (t). These signals satisfy the law of conservation of energy throughout the circuit, which implies that the sum of each of these instantaneous powers of different points in the circuit is zero. Reactive Power is then defined as the average DC-component value (mean) of the quadrature (instantaneous) power, pq(t), that was obtained from the product of the quadrature axis voltage and current signal. Note that in conventional power theory, although Reactive Power is defined as the peak of the non-energy related component of instantaneous power, it is typically measured and considered as an average DC-component (mean) of the instantaneous power in technical applications such as billing.
According to the present invention, when the power parameter to be measured is Apparent Power, it is defined as the RMS value of the complex instantaneous power given by Equation (1).
p(t)=pp(t)+ipq(t)xe2x80x83xe2x80x83(1)
where pp(t) is an instantaneous active power component
pq(t) is an instantaneous reactive power component
This definition of Apparent Power provides a consistent result in all system conditions, from single-phase sinusoidal to unbalanced three-phase systems with distorted waveforms. This consistency is unobtainable in other approaches.
In balanced three-phase systems with pure sinusoidal waveforms, the results obtained using the new approach are the same as those using conventional power theory.
In three-phase systems, since the new power theory is based on the sum of the instantaneous powers of three phases, then the measured Apparent Power, for example, is independent of the reference point voltage that is used in voltage measurement. This feature overcomes the conventional measurement methods problems described previously with respect to FIG. 1 and is unique when comprising with other definitions of Apparent Power cited in literature and standards.
Using conventional understanding, Reactive Power is defined as the peak value of one of the oscillatory components of the instantaneous power. The inventor has determined that that this cannot be obtained in frequency domain contrary to Plancherel""s Theorem. This discrepancy between frequency and time domain results leads to indeterminable quantities in the time and frequency domains, and is attributable to the fact that present power theory does not provide any information about Reactive Power in the frequency domain. Reactive Power as defined by the new approach is determined in both the time and frequency domains as an imaginary DC value, and the method is consistent for all system topologies.
The average (mean) values of the new instantaneous power on the real and the imaginary axes correspond to Active and Reactive Power respectively. Thus, in a method embodying the present invention, Reactive Power is defined and measured as a DC value and not as an ambiguous peak of one of the oscillatory components of instantaneous power.
Using the method embodying the present invention to determine the Active and Reactive Powers, it is demonstrated later that standard circuit theories are satisfied. The treatment of single-phase and three-phase systems are the same except that in three-phase systems the analysis is carried out on a per phase basis, and the total instantaneous power is obtained by adding together the three-phase results.
The 2-Norm, or RMS, of a signal is a measure of the size of that signal. Thus, Universal Apparent Power as determined by the method embodying the present invention is defined as the RMS of the complex instantaneous power. In three-phase balanced systems this definition leads to the standard definition of Universal Apparent Power that is three times the product of RMS of voltage and RMS of current.
However, using the method embodying the present invention in single-phase and unbalanced three-phase systems, the Universal Apparent Power is different from conventional Apparent Power, although it retains its basic dimension of volt-ampere. In fact, from the new approach it can be seen that in single-phase- systems the Universal Apparent Power is √2 times the RMS of voltage and current. This departure from the conventional Power Factor (which itself has little basis other than convention) is due to the AC components of the instantaneous power. In balanced three-phase systems the AC terms of the instantaneous power are cancelled.
Universal Power Factor determined by the method embodying the present invention is then considered as the ratio of Active Power to Universal Apparent Power as compared to conventional Power Factor. This leads to a reduced value for Universal Power Factor in a pure resistive single-phase circuit. In fact, for such a system the Universal Power Factor cannot be greater than 0.707 (1/√2). This reflects the consistency in the approach. This result, though arithmetically inconvenient, is shown to have a real basis in the analysis.
Symmetrical components have been used to analyses the new parameter definitions which are a feature of the present invention and a decomposition of different parameters in terms of the sequence components has been obtained. It is more technically acceptable for metering purposes that only the positive phase sequence voltage is considered in the analysis. This reflects the effects of unbalanced loads on the systems.
Preferably, the method further comprises filtering at least one of the instantaneous voltage and instantaneous current signals of the electrical power signal prior to their use in the calculating steps. In this way, several different but related parameters can be calculated by the same method steps with the appropriately filtered signals. More particularly, the filtering step preferably results in the fundamental frequency of the instantaneous voltage or the instantaneous current being obtained. Fundamental frequency filtered voltage signals enable the measured power parameter to be representative of network delivered power namely the power taken (used) by the load from the power supply.
It is to be appreciated that the present invention utilises at least the harmonics of one of the instantaneous voltage or the instantaneous current in combination with at least the fundamental frequency of the other instantaneous current or instantaneous voltage, to determine the power parameter. This covers three different situations namely: when one of the instantaneous voltage or current signals is unfiltered providing its full spectrum and the other is filtered; when both signals are unfiltered each providing the full frequency spectrum; and when one of the instantaneous voltage or current signals is filtered to provide its fundamental frequency spectrum and the other is filtered to provide its harmonic frequency spectrum. There is information in the harmonics of the instantaneous voltage or the instantaneous current which has previously been discarded that provides a more accurate measure of the power parameter.
By utilising the appropriate combination of filtered/unfiltered signals the following power parameters can be advantageously be calculated: Universal Apparent Power, Harmonic Apparent Power, Universal Distortion Factor, Voltage Distortion Power, Current Distortion Power, and Universal Power Factor.
The method may further comprise comparing a Network Delivered Power (NDP) Parameter, the Harmonic Apparent Power Parameter, the Voltage Distortion Power Parameter, or the Current Distortion Power Parameter with another power parameter determined by the method to produce a dimensionless figure of merit representative of the waveform distortion produced, in the electrical power signal by a load to which the electrical power signal is supplied. This is a particularly useful power parameter to measure as it provides information about where power supply distortion is being generated. For example, power parameters such as Voltage Distortion Factor and Current Distortion Factor can be determined.
When the electrical power signal comprises a balanced or unbalanced multiple-phase signal, the method preferably further comprises resolving the multiple-phase signal into a phase sequence for use in establishing the effect of the load on the electric power network. The phase sequence may comprise a positive-phase sequence in order to obtain a measure representative of the power generated at a source of the electrical power signal. Alternatively, the phase sequence may comprise negative and zero-phase sequences in order to obtain a measure representative of the power converted in the load. The method may also comprise using the positive, the negative and the zero-phase sequences to obtain a measure representative of the power used by the load.
The present invention also extends to a method of measuring a power parameter such as Apparent Power or Power Factor, of an electrical power signal the method comprising converting measured instantaneous voltage and current signals of the electrical power signal into the frequency domain and carrying out frequency spectrum analysis on the signals to derive the power parameter.
The method preferably further comprises: carrying out a relative phase-shift between the instantaneous voltage signal and the instantaneous current signal; and converting the relatively phase-shifted instantaneous voltage and current signals into the frequency domain for use in the frequency spectrum analysis.
Alternatively, the method further comprises: carrying out a relative phase-shift between the instantaneous voltage signal and the instantaneous current signal in the frequency domain for use in the frequency spectrum analysis.
The phase shift is important in order to be able to measure the imaginary (quadrature) component of the instantaneous power. In this way, the measurement of power quantities can be digitised and hence made significantly cheaper and more robust. The use of the frequency domain to calculate the power parameters also advantageously reduces the component counts in meters implementing the method.
Preferably, the frequency spectrum analysis involves carrying out a first convolution of the frequency spectra associated with the instantaneous voltage and current signals, a second convolution of the frequency spectra associated with the phase-shifted instantaneous voltage and current signals, and combining the results of the first and second convolutions.
According to another aspect of the present invention there is provided a method of measuring the value of an electrical power parameter, such as Apparent Power or Power Factor, of an electrical power signal the method comprising: converting an instantaneous voltage signal of the electrical power signal and an instantaneous current signal of the electrical power signal from the time domain into the frequency domain as frequency spectra; calculating a first instantaneous power spectrum as the convolution of the frequency spectra of the instantaneous voltage signal and the instantaneous current signal; carrying out a relative phase shift between the instantaneous voltage signal and the instantaneous current signal in the time domain; calculating a second instantaneous power spectrum as the convolution of the frequency spectra of the relatively phase-shifted instantaneous voltage and current signals; combining each of the first and second power spectra to determine the value of the electrical power parameter.
According to another aspect of the present invention, there is provided a method of measuring an electrical power parameter such as Apparent Power or Power Factor, of an electrical power signal, the method comprising: filtering at least one of an instantaneous voltage signal or an instantaneous current signal of the electrical power signal; using the filtered instantaneous voltage and current signal in: calculating first and second instantaneous power components as the respective products of non phase-shied/phase-shifted, instantaneous voltage and instantaneous current signals; RMS averaging each of the first and second instantaneous power components to determine their respective magnitudes; and using the calculated magnitudes to determine the value of the electrical power parameter.
In another aspect, the present invention provides a method of measuring a power quantity such as Apparent Power or Power Factor, of a multiple-phase electrical power signal, the method comprising: resolving the multiple-phase signal into a phase sequence for use in establishing the effect on the electrical power signal of a load to which the electrical power signal is supplied; using the phase sequence in: calculating first and second instantaneous power components as the respective products of non phase-shifted/phase-shifted, instantaneous voltage and instantaneous current signals; and RMS averaging each of the first and second power components to determine their respective magnitudes; and using the calculated magnitudes to determine the value of the electrical power parameter.
The present invention extends to an electrical power meter for measuring the value of an electrical power parameter, such as Apparent Power or Power Factor, of an electrical power signal, the meter comprising: means for calculating a first instantaneous power component as the product of an instantaneous voltage signal of the electrical power signal and an instantaneous current signal of the electrical power signal; means for implementing a relative phase shift between the instantaneous voltage signal and the instantaneous current signal; means for calculating a second instantaneous power component as the product of the relatively phase-shifted instantaneous voltage and instantaneous current signals; mean for RMS averaging each of the first and second power components to determine their respective magnitudes; and means for using the calculated magnitudes to determine the value of the electrical power parameter.